How to use this calculator
- Identify the measurements labelled Diagonal d. Check whether the figure satisfies the assumptions described below.
- Enter positive measurements in a common unit. Use the degree symbol convention for angles. Ratios such as eccentricity have no unit.
- Select Calculate. Inspect the result labels: lengths, areas and volumes have different dimensions. Copy the output or print the page if you need a record.
The formula
a = d/√2
Diagonal d = 7.0710678119
Worked example
For Diagonal d = 7.0710678119 cm, applying the displayed relationship gives side ≈ 5 cm. The remaining related measurements appear in the result panel. The example uses ideal dimensions and rounds only for display.
Model and limitations
Its diagonals are equal, perpendicular and bisect each other. Each diagonal has length a√2. The square has four lines of reflection symmetry and rotational symmetry through quarter-turns.
A diagonal is longer than a side. Square units describe area; a number in cm² must not be interpreted as cm. Inputs are limited to 10⁹ for lengths, 10¹⁸ for areas and 10²⁷ for volumes. Extremely thin or nearly degenerate figures may lose numerical accuracy; avoid treating displayed rounding as a measurement tolerance.